mining for spatial patterns

Shashi Shekhar Mining For Spatial Patterns 1

Mining for Spatial Patterns

Shashi Shekhar

Department of Computer Science University of Minnesota

http://www.cs.umn.edu/~shekhar

Collaborators: V. Kumar, G. Karypis, C.T. Lu, W. Wu, Y. Huang, V. Raju, P. Zhang, P. Tan, M. Steinbach

This work was partially funded by NASA and Army High Performance Computing Center


Spatial Data Mining(SDM) - Examples

Historical Examples:

London Asiatic Cholera 1854 (Griffith)

Dental health and fluoride in water, Colorado early 1900s

Current Examples:

Cancer clusters (CDC), Spread of disease (e.g. Nile virus)

Crime hotspots (NIJ CML, police petrol planning)

Environmental justice (EPA), fair lending practices

Upcoming Applications: Location aware services

Defense: Sensor networks, Mobile ad-hoc networks

Civilian: Mortgage PMI determination based on location


Army Relevance of SDM

StrategicPredicting global hot spots (FORMID)Army land: endangered species vs. training and war games Search for local trends in massive simulation data Critical infra-structure defense (threat assessment)

TacticalInferring enemy tactics (e.g. flank attack) from blobologyDetection of lost ammunition dumps (Dr. Radhakrishnan)

OperationalInterpretation of maps: map matching (locating oneself on map)

• identify terrain feature, e.g. ravines, valleys, ridge, etc.

Locating enemy (e.g. sniper in a haystack, sensor networks)Avoiding friendly fire


Spatial Data Mining(SDM) - Definition

Search of implicit, interesting patterns in geo-spatial data

Ex. Reconnaissance, Vector maps(NIMA, TEC), GPS, Sensor

networks

Data Mining vs. Statistics:

Primary vs. Secondary analysis

Global vs. local trends

Spatial Data Mining vs. Data Mining:

Spatial Autocorrelation

Continuous vs. Discrete data types


Background

Spatial Data MiningSpatial statistics in Geology, Regional EconomicsNSF workshop on GIS and DM (3/99) NSF workshop on spatial data analysis (5/02)

Spatial patterns: Spatial outliersLocation predictionAssociations, colocationsHotspots, Clustering, trends, …


Framework2 Approaches to mining Spatial Data

1. Pick spatial features; use classical DM methods2. Use novel data mining techniques

Our Approach:Define the problem: capture special needsExplore data using maps, other visualizationTry reusing classical DM methods If classical DM perform poorly, try new methodsEvaluate chosen methods rigourouslyPerformance tuning if needed


Spatial Association Rule

Citation: Symp. On Spatial Databases 2001Problem: Given a set of boolean spatial features

find subsets of co-located features, e.g. (fire, drought, vegetation)Data - continuous space, partition not natural, no reference feature

Classical data mining approach: association rulesBut, Look Ma! No Transactions!!! No support measure!

Approach: Work with continuous data without transactionizing it!

confidence = Pr.[fire at s | drought in N(s) and vegetation in N(s)] support: cardinality of spatial join of instances of fire, drought, dry veg.participation: min. fraction of instances of a features in join resultnew algorithm using spatial joins and apriori_gen filters


Event DefinitionConvert the time series into sequence of events at each spatial location.

Grid Cell (x,y) t1 t2 t3(1,1) Æ Æ Æ(1,2) {A, B, D} {D, L, J} Æ(1,3) Æ {A, B, E, G} {B, C, D}(1,4) {A, K, M} Æ Æ(2,1) {B, C, E} {E, G, M} {C, F, M}(2,2) Æ {C, E, F} {A, B, G, L}(2,3) Æ Æ Æ(2,4) {A, B} {D, F} {A, B, D}(3,1) Æ Æ Æ(3,2) {A, B, G} Æ {A, B, E}(3,3) {C, M} Æ Æ(3,4) Æ Æ Æ(4,1) Æ Æ Æ(4,2) Æ {D, K, L} Æ(4,3) Æ Æ {E, G, K}(4,4) Æ {A, B} {D, E, F}

DF A B

ABEG

DLJ

CEF

EGM

DKL

BCD

A BD

DEF

EGK

A BGL

ABE

CFM

t2 t3

time

A B

CM

A KM

A BD

A BG

BCE

t1

x

y


Interesting Association Patterns

Use domain knowledge to eliminate uninteresting patterns.A pattern is less interesting if it occurs at random locations.Approach:

Partition the land area into distinct groups (e.g., based on land-cover type).For each pattern, find the regions for which the pattern can be applied.If the pattern occurs mostly in a certain group of land areas, then it is potentially interesting.If the pattern occurs frequently in all groups of land areas, then it is less interesting.


Association Rules

Intra-zone non-sequential Patterns

Shrubland regionsFPAR-Hi NPP-Hi (support 10)

• Region corresponds to semi-arid grasslands, a type of vegetation, which is able to quickly take advantage of high precipitation than forests.

• Hypothesis: FPAR-Hi events could be related to unusual precipitation conditions.


Answers: and

Can you find co-location patterns from the following sample dataset?

Co-location


Spatial Co-location A set of features frequently co-

located

Given A set T of K boolean spatial feature

types T={f1,f2, … , fk}

A set P of N locations P={p1, …, pN } in a spatial frame work S, pi P is of some spatial feature in T

A neighbor relation R over locations in S

Find Tc = subsets of T frequently co-

located

Objective Correctness Completeness Efficiency

Constraints R is symmetric and reflexive Monotonic prevalence measure

Reference Feature Centric

Window Centric Event Centric

Co-location


Participation indexParticipation ratio pr(fi, c) of feature fi in co-location c = {f1, f2, …, fk}: fraction of instances of fi

withfeature {f1, …, fi-1, fi+1, …, fk} nearby 2.Participation index = min{pr(fi, c)}

AlgorithmHybrid Co-location Miner

Association rules Co-location rules

underlying space discrete sets continuous space

item-types item-types events /Boolean spatial features

collections transactions neighborhoods

prevalence measure support participation index

conditional probability measure

Pr.[ A in T | B in T ]

Pr.[ A in N(L) | B at L ]

Comparison with association rules

Co-location


Spatial Co-location Patterns

• Spatial feature A,B,C and their instances• Possible associations are (A, B), (B, C), etc.• Neighbor relationship includes following pairs:

•A1, B1•A2, B1•A2, B2•B1, C1•B2, C2

Dataset



Spatial feature A,B, C,and their instances

Support A,B =2 B,C=2 Support A,B=1 B,C=2

Partition approach[Yasuhiko, KDD 2001]

•Support not well defined,i.e. not independent of execution trace

•Has a fast heuristic which is hard to analyze for correctness/completeness

Dataset




Dataset Reference feature approach [Han SSD 95]

•C as reference feature to get transactions•Transactions: (B1) (B2)•Support (A,B) = Ǿ from Apriori algorithm

•Note: Neighbor relationship includes following pairs:•A1, B1•A2, B1•A2, B2•B1, C1•B2, C2




Our approach (Event Centric)• Neighborhood instead of transactions

• Spatial join on neighbor relationship

• Support Prevalence

•Participation index = min. p_ratio

•P_ratio(A, (A,B)) = fraction of instance of A participating in join(A,B, neighbor)

•ExamplesSupport(A,B)=min(2/2,3/3)=1

Support(B,C)=min(2/2,2/2)=1

Dataset




Support A,B =2 B,C=2

Support A,B=1 B,C=2

Support(A,B)=min(2/2,3/3)=1 Support(B,C)=min(2/2,2/2)=1

Partition approach

Our approachDataset

Reference feature approach

C as reference featureTransactions: (B1) (B2)Support (A,B) = Ǿ


Spatial OutliersSpatial Outlier: A data point that is extreme relative to it neighborsCase Study: traffic stations different from neighbors [SIGKDD 2001, JIDA 2002]Data - space-time plot, distr. Of f(x), S(x)Distribution of base attribute:

spatially smoothfrequency distribution over value domain: normal

Classical test - Pr.[item in population] is lowQ? distribution of diff.[f(x), neighborhood agg{f(x)}]Insight: this statistic is distributed normally!Test: (z-score on the statistics) > 2Performance - spatial join, clustering methods


Spatial Outlier DetectionGiven A spatial graph G={V,E} A neighbor relationship (K neighbors) An attribute function : V -> R An aggregation function : :R k -> R A comparison function Confidence level threshold Statistic test function ST: R ->{T, F}

Find O = {vi | vi V, vi is a spatial outlier}

Objective Correctness: The attribute values of vi

is extreme, compared with its neighbors

Computational efficiency

Constraints and ST are algebraic aggregate

functions of and Computation cost dominated by I/O

op.

f

aggrF

),( aggrdiff FfF

diffFf aggrF


Spatial Outlier Detection Test1. Choice of Spatial Statistic S(x) = [f(x)–E y N(x)(f(y))]

Theorem: S(x) is normally distributed

if f(x) is normally distributed

2. Test for Outlier Detection | (S(x) - s) / s | >

HypothesisI/O cost determined by clustering

efficiency

f(x) S(x)

Spatial Outlier Detection


Original Data

Variogram Cloud

Moran Scatter Plot

Graphical Spatial Tests


A Unified Approach Spatial Outliers

Original Data

Our Approach

Scatter Plot

•Tests : quantitative, graphical •Results:

•Computation = spatial self-join•Tests: algebraic functions of join•Join predicate: neighbor relations•I/O-cost: f(clustering efficiency)•Our algorithm is I/O-efficient for

Algebraic tests


Results 1. CCAM achieves higher

clustering efficiency (CE)

2. CCAM has lower I/O cost

3. High CE => low I/O cost

4. Big Page => high CE

Z-orderCCAM

I/O costCE value

Cell-Tree

Spatial Outlier Detection


Location Prediction

Citations: IEEE Tran. on Multimedia 2002, SIAM DM Conf. 2001, SIGKDD DMKD 2000Problem: predict nesting site in marshes

given vegetation, water depth, distance to edge, etc.

Data - maps of nests and attributesspatially clustered nests, spatially smooth attributes

Classical method: logistic regression, decision trees, bayesian classifier

but, independence assumption is violated ! Misses auto-correlation !Spatial auto-regression (SAR), Markov random field bayesian classifierOpen issues: spatial accuracy vs. classification accuraryOpen issue: performance - SAR learning is slow!


Given:1. Spatial Framework

2. Explanatory functions:3. A dependent class:4. A family of function

mappings:

Find: Classification model:

Objective:maximizeclassification_accuracy

Constraints: Spatial Autocorrelation

exists

},...{ 1 nssS RSf

kX :

},...{: 1 MC ccCSf

CRR ...

cf̂

),ˆ( cc ff

Nest locations Distance to open water

Vegetation durability Water depth

Location Prediction


Motivation and Framework


• Spatial Autoregression Model (SAR)• y = Wy + X +

• W models neighborhood relationships models strength of spatial dependencies error vector

• Solutions and - can be estimated using ML or Bayesian

stat.• e.g., spatial econometrics package uses

Bayesian approach using sampling-based Markov Chain Monte Carlo (MCMC) method.

• Likelihood-based estimation requires O(n3) ops.• Other alternatives – divide and conquer, sparse

matrix, LU decomposition, etc.

Spatial AutoRegression (SAR)


EvaluationLinear RegressionSpatial RegressionSpatial model is better

Xy

XWyy


• Markov Random Field based Bayesian Classifiers

• Pr(li | X, Li) = Pr(X|li, Li) Pr(li | Li) / Pr (X)

• Pr(li | Li) can be estimated from training data

• Li denotes set of labels in the neighborhood of si excluding labels at si

• Pr(X|li, Li) can be estimated using kernel functions

• Solutions• stochastic relaxation [Geman]• Iterated conditional modes [Besag]• Graph cut [Boykov]

MRF Bayesian


Experiment Design


Prediction Maps(Learning)MRF-P Prediction (ADNP=3.36) Actual Nest Sites (Real Learning)

MRF-GMM Prediction (ADNP=5.88) SAR Prediction (ADNP=9.80)

NZ=85 NZ=138

NZ=140 NZ=130


Prediction Maps(Testing)

Actual Nest Sites (Real Learning)

MRF-P Prediction (ADNP=2.84) Actual Nest Sites (Real Testing)

SAR Prediction (ADNP=8.63) MRF-GMM Prediction (ADNP=3.35) NZ=30 NZ=80

NZ=76 NZ=80


• SAR can be rewritten as y = (QX) + Q• where Q = (I- W)-1 which can be viewed as a spatial

smoothing operation.• This transformation shows that SAR is similar to

linear logistic model, and thus suffers with same limitations – i.e., SAR model assumes linear separability of classes in transformed feature space

• SAR model also make more restrictive assumptions about the distribution of features and class shapes than MRF

• The relationship between SAR and MRF are analogous to the relationship between logistic regression and Bayesian classifiers.

• Our experimental results shows that MRF model yields better spatial and classification accuracies than SAR predictions.

Comparison (MRF-BC vs. SAR)


Confusion Matrix:

Spatial Confusion Matrix:

MRF vs. SAR


Conclusion and Future Directions

Spatial domains may not satisfy assumptions of classical methods

data: auto-correlation, continuous geographic spacepatterns: global vs. local, e.g. spatial outliers vs. outliersdata exploration: maps and albums

Open Issues patterns: hot-spots, blobology (shape), spatial trends, …metrics: spatial accuracy(predicted locations), spatial contiguity(clusters)spatio-temporal datasetscale and resolutions sentivity of patternsgeo-statistical confidence measure for mined patterns

37

Army Relevance and Collaborations

•Relevance: “Maps are as important to soldiers as guns” - unknown•Joint Projects:

– High Performance GIS for Battlefield Simulation (ARL Adelphi)– Spatial Querying for Battlefield Situation Assessment (ARL Adelphi)

•Joint Publications: – w/ G. Turner (ARL Adelphi, MD) & D. Chubb (CECOM IEWD)– IEEE Computer (December 1996)– IEEE Transactions on Knowledge and Data Eng. (July-Aug. 1998)– Three conference papers

•Visits, Other Collaborations– GIS group, Waterways Experimentation Station (Army)– Concept Analysis Agency, Topographic Eng. Center, ARL, Adelphi

• Workshop on Battlefield Visualization and Real Time GIS (4/2000)


Reference1. S. Shekhar, S. Chawla, S. Ravada, A. Fetterer, X. Liu and C.T. Liu, “Spatial Databases: Accomplishments and

Research Needs”, IEEE Transactions on Knowledge and Data Engineering, Jan.-Feb. 1999.

2. S. Shekhar and Y. Huang, “Discovering Spatial Co-location Patterns: a Summary of Results”, In Proc. of 7th International Symposium on Spatial and Temporal Databases (SSTD01), July 2001.

3. S. Shekhar, C.T. Lu, P. Zhang, "Detecting Graph-based Spatial Outliers: Algorithms and Applications“, the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2001.

4. S. Shekhar, C.T. Lu, P. Zhang, “Detecting Graph-based Saptial Outlier”, Intelligent Data Analysis, To appear in Vol. 6(3), 2002

5. S. Shekhar, S. Chawla, the book “Spatial Database: Concepts, Implementation and Trends”, Prentice Hall, 2002

6. S. Chawla, S. Shekhar, W. Wu and U. Ozesmi, “Extending Data Mining for Spatial Applications: A Case Study in Predicting Nest Locations”, Proc. Int. Confi. on 2000 ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery (DMKD 2000), Dallas, TX, May 14, 2000.

7. S. Chawla, S. Shekhar, W. Wu and U. Ozesmi, “Modeling Spatial Dependencies for Mining Geospatial Data”, First SIAM International Conference on Data Mining, 2001.

8. S. Shekhar, P.R. Schrater, R. R. Vatsavai, W. Wu, and S. Chawla, “Spatial Contextual Classification and Prediction Models for Mining Geospatial Data”,To Appear in IEEE Transactions on Multimedia, 2002.

9. S. Shekhar, V. Kumar, P. Tan. M. Steinbach, Y. Huang, P. Zhang, C. Potter, S. Klooster, “Mining Patterns in Earth Science Data”, IEEE Computing in Science and Engineering (Submitted)


Reference10. S. Shekhar, C.T. Lu, P. Zhang, “A Unified Approach to Spatial Outliers Detection”, IEEE Transactions on

Knowledge and Data Engineering (Submitted)

11. S. Shekhar, C.T. Lu, X. Tan, S. Chawla, Map Cube: A Visualization Tool for Spatial Data Warehouses, as Chapter of Geographic Data Mining and Knowledge Discovery. Harvey J. Miller and Jiawei Han (eds.), Taylor and Francis, 2001, ISBN 0-415-23369-0.

12. S. Shekhar, Y. Huang, W. Wu, C.T. Lu, What's Spatial about Spatial Data Mining: Three Case Studies , as Chapter of Book: Data Mining for Scientific and Engineering Applications. V. Kumar, R. Grossman, C. Kamath, R. Namburu (eds.), Kluwer Academic Pub., 2001, ISBN 1-4020-0033-2

13. Shashi Shekhar and Yan Huang , Multi-resolution Co-location Miner: a New Algorithm to Find Co-location Patterns in Spatial Datasets, Fifth Workshop on Mining Scientific Datasets (SIAM 2nd Data Mining Conference), April 2002

mining for spatial patterns

Documents

spatial data analysis

geospatial data

spatial location

continuous data

spatial joins

spatial data1

spatial databases

special needsexplore